CAREER: Physics-Oriented Statistical Wave Analysis Integrating Order and Chaos

无线通信、电子和传感器系统预计将在日益拥挤、竞争激烈和竞争激烈的环境中出现。无线通信不断发展的复杂性要求对现有的电磁波分析和建模方法进行根本性的改变。通常情况下，对波系统、辐射噪声源和传播环境没有精确的了解。此外，在短波长范围内，电磁波散射过程可能对细节非常敏感。它导致波分布的非常高的可变性，并且使得确定性解仅与特定配置相关。该项目提出了新的面向物理的统计电磁波模型，以解决环境的不确定性。这项研究为设计无线设备和天线时利用传播环境的复杂性开辟了新的途径。这些成果将建立一个可配置的虚拟测试平台，用于在不受实验室测量限制的复杂环境中进行通信。研究进展将与教育相结合，开发非传统的教育工具。该项目将在新墨西哥州大学（UNM）创建一个虚拟现实电磁实验室，通过创新的数据可视化和交互式模拟提供多方面的教学和学习环境。其他教育部分包括开发在线课程和高级跨学科课程，通过UNMTemps青年暑期计划指导高中生，并通过与UNM的国家资助的多元文化工程计划和新墨西哥州少数民族参与联盟合作，扩大代表性不足的群体的参与。本研究的目的是探讨复杂电磁环境下统计波分析的基本数学模型和计算算法。该项目将研究一个创新的理论解决方案，麦克斯韦方程的波动混沌介质（域表现出射线混沌动力学）。基本解（随机绿色函数）严格集成的相干和非相干的传播在一个紧凑的形式。提出了一种新的随机积分方程方法来研究统计波在混沌环境中的传播。利用随机矩阵理论定量解释了波浪混沌的普遍统计性质。由于现实世界的电磁系统往往表现出混合混沌和规则的波动动力学，工作的第二部分研究的第一性原理理论框架相结合的可积（规则）和不可积（混沌）波动动力学。通过将组件，网站和系统的具体信息与普遍的混沌动力学，工作完成了一个全面的框架，复杂的波系统的统计分析和不确定性量化。这些进步将建立一个必要的模拟驱动，混沌下的设计能力，预计将在工程学科产生重大影响。该项目的知识将带来新一代计算机辅助设计（CAD）工具，这将彻底改变复杂环境中的电磁仿真，预测，设计和优化。虽然拟议的研究主要集中在电动力学，但该方法可应用于其他领域，包括声学和振动，量子介观输运和核物理。

Wireless communications, electronics, and sensor systems are expected to take place in increasingly congested, contested, and competitive environments. The evolving complexity of wireless communications demands fundamental changes to existing electromagnetic wave analysis and modeling methodologies. Often at times, there is no precise knowledge of the wave system, the radiating noise source, and the propagation environment. Furthermore, in the short-wavelength regime, the electromagnetic wave scattering process can be very sensitive to details. It results in a very high variability of wave distributions, and makes the deterministic solution relevant only to the specific configuration. This project proposes new physics-oriented statistical electromagnetic wave models to resolve environmental uncertainties. The proposed research opens up new pathways to exploit the complexity of propagation environments when designing wireless devices and antennas. The outcomes will establish a configurable virtual testbed for communications in complex environments not confined by the laboratory measurements. The research advancements will be integrated with the education to develop unconventional educational tools. The project will create a virtual reality electromagnetic laboratory at University of New Mexico (UNM), which offers a multifaceted teaching and learning environment through innovative data visualization and interactive simulation. Other educational components include developing online courses and advanced cross-disciplinary courses, mentoring high school students through UNMTemps Youth Summer program, and broadening participation of underrepresented groups by working with UNM's state-funded Multicultural Engineering Program and the New Mexico Alliance for Minority Participation. The objective of this research is to investigate fundamental mathematical models and computational algorithms for the statistical wave analysis in complex electromagnetic environments. The project will study an innovative theoretical solution to Maxwell's Equations in the wave-chaotic media (domains exhibiting ray-chaotic dynamics). The fundamental solution (stochastic Green's function) rigorously integrates the coherent and incoherent propagations within a compact form. A new stochastic integral equation method is proposed for the statistical wave propagation through the chaotic environment. It quantitatively interprets the universal statistical properties of wave chaos through the random matrix theory. Since real-world electromagnetic systems often exhibit mixed chaotic and regular wave dynamics, the second part of the work investigates the first-principles theoretical framework of combing the integrable (regular) and non-integrable (chaotic) wave dynamics. By incorporating the component-, site-, and system-specific information with the universal chaotic dynamics, the work accomplishes a comprehensive framework for the statistical analysis and uncertainty quantification of complex wave systems. The advancements will establish an imperative simulation-driven, design-under-chaos capability, which is expected to have a big impact in the engineering discipline. Knowledge from this project will bring forth a new generation of computer-aided design (CAD) tools that will revolutionize electromagnetic simulation, prediction, design and optimization in complex environments. While the proposed research primarily focuses on electrodynamics, the methodology can be applied to other fields including acoustics and vibrations, quantum mesoscopic transport, and nuclear physics.